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人気のある三角関数 >

sec^2(x)csc(x)-2csc(x)=2-sec^2(x)

解

sec^{2} (x) csc (x) - 2 csc (x) = 2 - sec^{2} (x)

解

x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn, x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

+1

度

x = 13 5^{\circ} + 36 0^{\circ} n, x = 22 5^{\circ} + 36 0^{\circ} n, x = 4 5^{\circ} + 36 0^{\circ} n, x = 31 5^{\circ} + 36 0^{\circ} n

解答ステップ

sec^{2} (x) csc (x) - 2 csc (x) = 2 - sec^{2} (x)

両辺から

2 - sec^{2} (x)

を引く

sec^{2} (x) csc (x) - 2 csc (x) - 2 + sec^{2} (x) = 0

因数

sec^{2} (x) csc (x) - 2 csc (x) - 2 + sec^{2} (x) : (sec (x) + 2) (sec (x) - 2) (csc (x) + 1)

sec^{2} (x) csc (x) - 2 csc (x) - 2 + sec^{2} (x)

= (sec^{2} (x) csc (x) - 2 csc (x)) + (sec^{2} (x) - 2)

csc (x)

を

sec^{2} (x) csc (x) - 2 csc (x) : csc (x) (sec^{2} (x) - 2)

からくくり出す

sec^{2} (x) csc (x) - 2 csc (x)

共通項をくくり出す

csc (x)

= csc (x) (sec^{2} (x) - 2)

= (sec^{2} (x) - 2) + csc (x) (sec^{2} (x) - 2)

共通項をくくり出す

sec^{2} (x) - 2

= (sec^{2} (x) - 2) (csc (x) + 1)

因数

sec^{2} (x) - 2 : (sec (x) + 2) (sec (x) - 2)

sec^{2} (x) - 2

累乗根の規則を適用する:

a = (a)^{2}

2 = (2)^{2}

= sec^{2} (x) - (2)^{2}

2乗の差の公式を適用する:

x^{2} - y^{2} = (x + y) (x - y)

sec^{2} (x) - (2)^{2} = (sec (x) + 2) (sec (x) - 2)

= (sec (x) + 2) (sec (x) - 2)

= (sec (x) + 2) (sec (x) - 2) (csc (x) + 1)

(sec (x) + 2) (sec (x) - 2) (csc (x) + 1) = 0

各部分を別個に解く

sec (x) + 2 = 0 or sec (x) - 2 = 0 or csc (x) + 1 = 0

sec (x) + 2 = 0 : x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

sec (x) + 2 = 0

2

を右側に移動します

sec (x) + 2 = 0

両辺から

2

を引く

sec (x) + 2 - 2 = 0 - 2

簡素化

sec (x) = - 2

sec (x) = - 2

以下の一般解

sec (x) = - 2

sec (x)

2 πn

循環を含む周期性テーブル :

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

sec (x) - 2 = 0 : x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

sec (x) - 2 = 0

2

を右側に移動します

sec (x) - 2 = 0

両辺に

2

を足す

sec (x) - 2 + 2 = 0 + 2

簡素化

sec (x) = 2

sec (x) = 2

以下の一般解

sec (x) = 2

sec (x)

2 πn

循環を含む周期性テーブル :

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

csc (x) + 1 = 0 : x = \frac{3 π}{2} + 2 πn

csc (x) + 1 = 0

1

を右側に移動します

csc (x) + 1 = 0

両辺から

1

を引く

csc (x) + 1 - 1 = 0 - 1

簡素化

csc (x) = - 1

csc (x) = - 1

以下の一般解

csc (x) = - 1

csc (x)

2 πn

循環を含む周期性テーブル:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

x = \frac{3 π}{2} + 2 πn

x = \frac{3 π}{2} + 2 πn

すべての解を組み合わせる

x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn, x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn, x = \frac{3 π}{2} + 2 πn

equationは以下で未定義のため:

\frac{3 π}{2} + 2 πn

x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn, x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

グラフ

人気の例

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2 sin (x) = - 2, 0 \leq x \leq 2 π

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csc (a) = 5

1-1/2 cos(2x-pi/2)=0

1 - \frac{1}{2} cos (2 x - \frac{π}{2}) = 0

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